Mississippi Math A3.N.1

MathGrades 9–12Number and Quantity (N) Explore and Illustrate the Characteristics and Operations Connecting Sequences and Series

The Standard

Express sequences and series using recursive and explicit formulas.

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students write one rule to get each term from the term before it and another to get a term from its position. They write both kinds of rules for the running total of the first n terms.
What Mastery Looks Like: For 4, 7, 10, ... they write a_1 = 4, a_n = a_(n-1) + 3, and a_n = 4 + 3(n-1). They write S_1 = 4, S_n = S_(n-1) + a_n, and S_n = n(3n+5)/2. They check that S_3 = 21, not 10.
Common Misconceptions: Students confuse the nth term with the sum of the first n terms. They leave out the starting value in a recursive rule or use n instead of n-1 in an explicit rule. They may mistake a constant difference for a constant ratio.
How to Assess It: Exit ticket: For 3, 6, 9, ... write recursive and explicit rules for the terms and for their running total. Find the fifth term and the sum of the first five terms.

Lesson moves

Have pairs build rows of 2, 4, and 6 counters, then write rules for each row and the total after each row.
Ask students why the fifth term and the sum of five terms in 5, 10, 15, ... need different formulas.
Have teams match cards showing 3, 6, 9, ..., its recursive and explicit term rules, and its running-total formula.
Post weekly deposits of $10, $15, $20, ...; students write term and running-total rules and predict the total after eight weeks.

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